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MonusLaws.scala
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MonusLaws.scala
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/*
* Copyright 2021 Arman Bilge
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package schrodinger.laws
import algebra.ring.AdditiveCommutativeMonoid
import cats.kernel.laws.*
import schrodinger.math.Monus
import schrodinger.math.syntax.*
trait MonusLaws[A](using val A: Monus[A]):
private given AdditiveCommutativeMonoid[A] = A.additiveCommutativeMonoid
import given_AdditiveCommutativeMonoid_A.*
def monusAxiom1(x: A, y: A) = x + (y ∸ x) <-> y + (x ∸ y)
def monusAxiom2(x: A, y: A, z: A) =
(x ∸ y) ∸ z <-> x ∸ (y + z)
def monusAxiom3(x: A) = (x ∸ x) <-> zero
def monusAxiom4(x: A) = (zero ∸ x) <-> zero
def monusNaturalOrderConsistency(x: A, y: A) =
A.naturalOrder.lteqv(x, x + y)
object MonusLaws:
def apply[A: Monus]: MonusLaws[A] = new MonusLaws {}